{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:LFQR7BQIO53DOT4PDMUEDXREJP","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2a4b1759423c00ae1ffa463e00c2edc08c4bd00e4cca1b8bfe6fc924c9dc6a9d","cross_cats_sorted":["cs.NA","math.AP","math.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-04-10T14:04:06Z","title_canon_sha256":"4aed9379f07cb6022f8cc4c77a52a26faeffc651f9bcf75cf6437e38bae7091b"},"schema_version":"1.0","source":{"id":"2404.07015","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.07015","created_at":"2026-07-05T08:06:34Z"},{"alias_kind":"arxiv_version","alias_value":"2404.07015v1","created_at":"2026-07-05T08:06:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.07015","created_at":"2026-07-05T08:06:34Z"},{"alias_kind":"pith_short_12","alias_value":"LFQR7BQIO53D","created_at":"2026-07-05T08:06:34Z"},{"alias_kind":"pith_short_16","alias_value":"LFQR7BQIO53DOT4P","created_at":"2026-07-05T08:06:34Z"},{"alias_kind":"pith_short_8","alias_value":"LFQR7BQI","created_at":"2026-07-05T08:06:34Z"}],"graph_snapshots":[{"event_id":"sha256:0e0ed6c6a0e3324e70ae48f7c075efa027c1c18cc8e36b5424fd25763036991c","target":"graph","created_at":"2026-07-05T08:06:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2404.07015/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The work is organized as follows. First an introduction is given in Chapter 1. In Chapter 2 we introduce the POD method in finite and infinite-dimensional Hilbert spaces and discuss various applications. Chapter 3 is devoted to to POD-based Galerkin schemes for evolution problems. Mainly, we study linear problems taking different discretization methods into account. We provide a certified a-priori and a-posteriori error analysis. Furthermore, the numerical realizations are explained and illustrated by test examples. Quadratic programming problems governed by liner evolution problems are invest","authors_text":"Dennis Beermann, Luca Mechelli, Stefan Banholzer, Stefan Volkwein","cross_cats":["cs.NA","math.AP","math.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-04-10T14:04:06Z","title":"POD Suboptimal Control of Evolution Problems: Theory and Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.07015","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c3cb33f35b63ca63ab33344035c8e1b6d24e6184f80ba8801fbb59e0438d14af","target":"record","created_at":"2026-07-05T08:06:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2a4b1759423c00ae1ffa463e00c2edc08c4bd00e4cca1b8bfe6fc924c9dc6a9d","cross_cats_sorted":["cs.NA","math.AP","math.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-04-10T14:04:06Z","title_canon_sha256":"4aed9379f07cb6022f8cc4c77a52a26faeffc651f9bcf75cf6437e38bae7091b"},"schema_version":"1.0","source":{"id":"2404.07015","kind":"arxiv","version":1}},"canonical_sha256":"59611f86087776374f8f1b2841de244bdb8391b6a8c93cf444283761b77773d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59611f86087776374f8f1b2841de244bdb8391b6a8c93cf444283761b77773d4","first_computed_at":"2026-07-05T08:06:34.001946Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:06:34.001946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wuHSngw+hwIYRB5fsVztw++LG1PXOGyG2BrlE2bKt/LEqmR4bJWcK+zeLZJ/NI2aNAZXrcqpcbnlSoK8SlDpCw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:06:34.002416Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.07015","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3cb33f35b63ca63ab33344035c8e1b6d24e6184f80ba8801fbb59e0438d14af","sha256:0e0ed6c6a0e3324e70ae48f7c075efa027c1c18cc8e36b5424fd25763036991c"],"state_sha256":"0f2089a9b4752608699ef73ecb29626174afc9d3a08b5e67f810bd7f18acacbe"}